# The value of ( f ∘ g ) ( x ) and the value of ( f ∘ g ) ( 2 ) if g ( 2 ) is 5 and f ( 5 ) is 12. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.6, Problem 2E
To determine

## To evaluate: The value of (f∘g)(x) and the value of (f∘g)(2) if g(2) is 5 and f(5) is 12.

Expert Solution

The value of (fg)(x) is f(g(x)) and the value of (fg)(2) is 12.

### Explanation of Solution

The function fg is called the compositions of functions f and g and the domain of fg is set of all x in the domain of g such that g(x) is in the domain of f, that means,

(fg)(x)=f(g(x))

Thus, by above definition, the value of (fg)(x) is f(g(x)) .

Calculation:

From Section1,

(fg)(x)=f(g(x)) (1)

Substitute 2 for x in above formula,

(fg)(2)=f(g(2))

The value of g(2) is 5, substitute 5 for g(2) in above values,

(fg)(2)=f(5)

The value of f(5) is 12, substitute 12 for f(5) in above values,

(fg)(2)=12

Thus, the value of (fg)(2) is 12.

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